Invariant Regularization of Supersymmetric Chiral Gauge Theory

TL;DR

This paper introduces a regularization scheme for supersymmetric chiral gauge theories that preserves supersymmetry and gauge covariance, automatically restores gauge invariance when anomalies cancel, and aids in analyzing various anomalies and their algebraic structures.

Contribution

It proposes a novel regularization scheme that maintains supersymmetry and gauge covariance, enabling automatic gauge invariance restoration and improved anomaly analysis.

Findings

Regularization scheme respects supersymmetry and gauge covariance.

Automatic gauge invariance restoration under anomaly cancellation.

Application to various anomalies and algebraic structures in supersymmetric theories.

Abstract

We present a regularization scheme which respects the supersymmetry and the maximal background gauge covariance in supersymmetric chiral gauge theories. When the anomaly cancellation condition is satisfied, the effective action in the superfield background field method automatically restores the gauge invariance without counterterms. The scheme also provides a background gauge covariant definition of composite operators that is especially useful in analyzing anomalies. We present several applications: The minimal consistent gauge anomaly; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and an anomalous supersymmetric transformation law of the supercurrent (the ``central extension'' of N=1 supersymmetry algebra) and of the R-current.